Assuming you've done the above (which will let you type Japanese in any document), you'll be able to enter Japanese text in a Word document (Word 2004, anyway). You might have to select a Japanese font manually, although it's supposed to do it for you when you switch input methods. You can also "Japanize" Word by dropping it on the "Microsoft Langauge Register" application in the Extras folder, but that's not a requirement.
It's worth noting that any application that uses OSX's built-in Unicode text rendering system (for example TextEdit, Mellel, Safari, Mail, Camino, the Finder, or most modern apps that handle lots of words) will have zero propblem switching languages within a document or using any font in any language you throw at it. OSX really has a great multilingual system.
Word, however, uses its own text rendering system, and does not treat non-roman characters quite as smoothly.
If you do a lot of multilingual word processing, I'd highly recommend getting yourself Mellel, iWork, or another modern app that handles Unicode text properly. Might not have quite the bells and whistles of Word, but much easier to deal with, and the .rtf files that most of these programs produce can be read by other Word users if that's an issue.